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arXiv · 2402.16334

On the algebra generated by three commuting matrices: combinatorial cases

Ron Cherny·Matthew Satriano·Yohan Song
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Abstract

Gerstenhaber proved in 1961 that the unital algebra generated by a pair of commuting $d\times d$ matrices over a field has dimension at most $d$. It is an open problem whether the analogous statement is true for triples of matrices which pairwise commute. We answer this question for special classes of triples of matrices arising from combinatorial data.

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Ron Cherny, Matthew Satriano, Yohan Song. 2024-02-26. On the algebra generated by three commuting matrices: combinatorial cases. https://arxiv.org/abs/2402.16334

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